**Connection** to be a path from \(A\) to \(B\) through a certain city \(C\). \(A\) and \(B\) do not have to be distinct (i.e. sightseers going to a city then returning), though \(A \rightarrow C \rightarrow B\) is distinct from \(B \rightarrow C \rightarrow A\). Find the number of possible connections in this state.

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